FIG. 1 shows a wireless communication system comprising a base station with M transmit antennae in communicative contact with K users/receivers. Each of the K receivers has Nk (k=1, 2, . . . , K) receiver antennae. The base station sends K data streams simultaneously to K receivers such that each receiver receives one data stream. At the transmitter side, the signal vector s is precoded by a precoder P to produce a transmitted vector x. A linear receive combiner for combining the signals received through multiple receive antennae is provided in each receiver to improve reception quality. Following receiver combination the combined signal is input into a data detector.
The system shown in FIG. 1 can be mathematically described in the following form. Let Hk (of size Nk×M) and ck (of size 1×Nk) be the channel matrix and receiver combining vector of receiver k. The effective channel of receiver k as seen by the base station is:ĥk=ckHk  (1)
To keep the noise power unchanged, the norm of the combining vectors are all 1, i.e. ∥ck∥=1.
The effective channel matrix is:
                              H          ^                =                  [                                                                                          h                    ^                                    1                                                                                    ⋮                                                                                                          h                    ^                                    K                                                              ]                                    (        2        )            
If base station employs linear minimum mean square error (MMSE) precoding, then the precoding matrix P can be expressed as:
                    P        =                                            β              ⁡                              (                                                                                                    H                        ^                                            H                                        ⁢                                          H                      ^                                                        +                                                            K                                              E                        ir                                                              ⁢                                          I                      M                                                                      )                                                    -              1                                ⁢                                    H              ^                        H                                              (        3        )            where Etr is the total transmit power, IM is an M×M identity matrix and the superscript H denotes a matrix transpose conjugate operation. β is a power normalisation factor given by:
                              β          =                                                    E                ir                                            tr                (                                                      F                                          -                      2                                                        ⁢                                                            H                      ^                                        H                                    ⁢                                      H                    ^                                                                                      ⁢                                  ⁢                  where          ⁢                      :                                              (        4        )                                F        =                                                            H                ^                            H                        ⁢                          H              ^                                +                                    K                              E                ir                                      ⁢                          I              M                                                          (        5        )            
Let yi,k be the received signal at antenna i of receiver k. The combined receive signal of receiver k follows:zk=ck[y1,ky2,k . . . yNk,k]T  (6)
The linear zero-forcing (ZF) precoder proposed in the above mentioned Joham et al and the Peel et al papers can be obtained by removing the term
      K          E      ir        ⁢      I    M  in equations (3) and (5).
It is desirable to design linear receiver combining vectors ck for a given set of receivers such that the total distortion, measured by the sum of mean square error (MSE) of all receivers, is minimized. Solutions to this problem are known.
In some known methods the combining vectors are selected by taking the left singular vector corresponding to the dominant singular value of receivers' channel matrices. This method may suffer from significant performance loss since the combining vectors of receivers are not jointly designed.
Another method of exploiting the diversity of multiple receive antennas is antenna selection.